Ion conduction in the KcsA potassium channel analyzed with a minimal kinetic model

We use a model by Nelson to study the current-voltage and conductance-concentration curves of bacterial potassium channel KcsA without assuming rapid ion translocation. Ion association to the channel filter is rate controlling at low concentrations, but dissociation and transport in the filter can limit conduction at high concentration for ions other than ${\mathrm{K}}^{+}$. The absolute values of the effective rate constants are tentative but the relative changes in these constants needed to qualitatively explain the experiments should be of significance.

Figure 1

Schematic view of the conduction steps in the ion channel according to Nelson [15] (we do not assume rapid ion translocation and introduce $\delta =0$).

Figure 2

$J\text{−}V$ curves for ${\mathrm{K}}^{+}$ symmetrical solutions of different concentration $S$ obtained from Eq. (2b) with ${\nu }_a=16\times {10}^8{\mathrm{M}}^{-1}{\mathrm{s}}^{-1}$ and $k_d=4\times {10}^8{\mathrm{s}}^{-1}$. The dashed curve with $S=0.8M$ corresponds to conduction when both ion dissociation and translocation are rate limiting [Eq. (2a) with $k_t=k_d$].

Figure 3

$J\text{−}V$ curves for ${\mathrm{K}}^{+}$, ${\mathrm{Tl}}^{+}$, ${\mathrm{Rb}}^{+}$, and ${\mathrm{Na}}^{+}$ in symmetrical solutions of ionic concentration $S=0.1M$.

Figure 4

$g\text{−}S$ curves for ${\mathrm{K}}^{+}$, ${\mathrm{Tl}}^{+}$, ${\mathrm{Rb}}^{+}$, and ${\mathrm{Na}}^{+}$ in symmetrical solutions of ionic concentration $S$ at transmembrane voltage $V=200\mathrm{mV}$ for the same rate constants of Fig. 3.